I have used both types of cameras. I think they are both good. With my powershot (it is a few years old) it takes AA batteries which is convenient if you need to get new batteries you can just buy them in the park, although they would be expensive. I have used just regular AA batteries (not lithium) and they last me a while, even with the screen on. I wouldn't worry about it running out during the day.
The coolpix I have used has a rechargeable battery, which as long as you charge at night, you should be all set all day. The batteries lasted I think like three days before I had to charge the battery, but I would recommend charging every night just to be on the safe side.
They both take really good pictures, and I would recommend either kind. It is more a personal preference, and how they feel to you. Hope that helped!